If d y ~d x =y+3, y+3 0 and y(0)=2 , then y( 2) is equal to

Step-by-step solution

aligned & d y ~d x =y+3 & ~d y y+3 = d x aligned Integrating on both sides, we get d y y+3 = d x+ c array ll & (y+3)=x+ c ...(i) & y=2 when x=0 & (2+3)=0+ c c = 5 & (y+3)=x+ 5...[From(i)] & y+3=5 e ^x & y=5 e ^x-3 & y( 2)=5 e ^ 2 -3=10-3=7 array ...[From (i)]